The Baro-Buret-A New Accurate Gas Buret' Harold S i m m o n s Booth

ITORLEY CIiE\lIC.\L. ~ . . A B O R i l ' O R > ~ . \ rESTER\ . RESERVE USIIGRSITY. Cl .EVEL.ASD, Of110

HERE have heen at- tempts to improre the T gas buret since its in-

ception. The chief improve- iiients haye heeii the derelop- inelit, of devicps of one sort or another to cornpelisate for t e m p e r a t u r e and pressure errors, of which that devel- oped by Wii te i l I ) is one of the best.

The sources of errors ill tlie gas buret are fairly obvious:

(1) The m e a s u r e m e n t of

There i s described t h e construct ion and use of a new gas bu re t , t h e baro-buret , i n which t h e b u r e t becomes the well of a barometer , thus enabl ing t h e experimenter t o read both pressure and volume s imultaneously wi th greatly increased accuracy and speed. Since w i t h this i n s t r u m e n t t h e volume m a y be measured a t a n y de- sired pressure, t h e accuracy of reading smal l volumes is especially increased.

T h e errors and l imitat ions are discussed, including the m a x i m u m error possible under the m o s t favorable conditions for m i n i m u m error.

The combinat ion of t h e measurement of pressure and volume i n o n e instrument opens up m a n y a p - plications, some of which are given.

The l i a r o h r e t to hc clc- s c r i b e d eliminate> all thest. difficulties.

Obviously tlic caliief diffi- culty lie- in the establishiitriit arid maintenancr of tlie Tori- celliari vacuum in thc ti arc^- m e t r ic column. The coni- b i n a t i o n of the o~-erflon- method first applied in tliv Toepler pump arid later to t 11 e I] a r o rrie t e r del-isetl 11)- Germanri (;), with tlie ga- buret offered 110 s p i t ) i l i t ie- .

pressure by balancing the mer- cury column against the atmosphere and by reading the pressure of the atmosphere separately on the barometer increases enor- mously the errors in pressure reading.

(2) Accurate adjustment of the mercury levels in reading the volume is fraught with difficulty.

( 3 ) Accurate temperature control is impractical. (4) Leaks in the rubber connections and leaking of gas into

the buret through the rubher tubing connecting the biiret to the level tube is a hidden source of error.

The experimenter is limited to the measurement of the gases a t atmospheric pressure or else may espect serious errors due to leaks.

The use of a compensator introduces errors due to the volume of gas imprisoned in the compensator. In the n'hite buret, however, this error is minimized

Of these tlifficultieb the first two are probatily tlic iiici>t

Several years ago it occurred to tlie writer that tliesr difficiil- ties might he eliiiiinated by an arrangement wheretiy the pressure of the gas in the buret was lialanced liy the prewiirc of a colunin of mercury oiilys rather than by tlie pressuw of the atniospliere. 111 other words. tlir gas lxiret cor i ld Iir made the well of a harometer. There have been m w a l efforts to arcomplisli this, hiit they have all resulted i t1 clutiisy. complicated apparatus. difficult to make and to iiiaiiitaiti. Oiie of the. earliest of these wa:, del-ked by Fraiiklatid aiitl Ward ((;), BIore receiitly I3oue and Kheeler 2 , .j) tiiodified Franklaiitl'h buret but liniited it-: usefulne-:s. 13oiic :md Theeler 's buret is oi tlie coiistaiit-\-olluli~ t y i e aiitl ~ufYers from the follon.iiig defects:

(1) On account of set volume marks the buret ha< a lice limited to ordinary gas analysis.

( 2 ) There is no provision for preventing chance hubl~l from the rubber tuhing used to connect the level hull) from ri ing into the buret.

The diameter of the buret and pressure cidumn k too small and may easily vitiate the measurements on account of the capillary-depression effect.

On account of the short length of the pressurc column, the manipulator has practically little choice of pressures a t which to measure the gas; thus there is no flesihility of mmsurc- ment with it.

The vacuum in the pressure-reading column i-; produced hy piimping out the gas through a stopcock at the top of the column and is maintained by shutting the stopcock. hIorkv said that "a stopcock is a located leak," and frequently, when you depend upon them, as in this case, they dexrve stronger language.

Presented before t h e Divi, ion of Physi- cal a n d Inorganic Chemistry at the 67th Mestin: of t h e American Chemical Society, LVashington D C., .April 21 t o 26. 1924 Revised pap?r recei,.ed March 11, 1833. Abstracted i n Science , 59, 5 5 3 (1924'

( 5 )

( 6 )

. serious.

( 3 )

(4)

(5)

1 Received August 27, 1927.

- The practical del-elopinelit

of thi. idea iwulted ii i tlie "baro-buret," l~hic l i has l)eeti found to he. not only accurate, but also rapid and capahlr of n-ide application. It has been thoroughly tested in this laboratory for seveii years and has heeii applied to iiiitiieroii': prl)blelns sllcc~ssi'ully.

Design

The I)aru-lliirc~t cousists essentially of two hil ls: the 100- (T. calibrated gas Iiuret, K . and the barometric coliiiiiti. K . made of glass tubing of the $a im hure as the liuret, so that tlie clepressioii of the mercury due to surface tension dial1 be the satiie in both tubes. (Figures 1 and 3) These tno part? are coiiiiected by the F t O p c f J C k S .If and -1- by fused- glass coiiiiectioiis. and through preswre rubber tuhiiig t o the nierciiry re>ervoir, R. The tube coniposing the t r a p L . s h o u l d slope dightly towards tlie I)uret s:) tliat gas I)iilil)lc> leaking tlirougli the rubber tuhing n i l1 c*)llrct in the t rap rather than go up the side tube..

At first it was feared that there wdd he sufficient sti,aiti to Iircak fused coiinections tietveen the part> of the h i re t . aiitl cwiiiectioiis of rubher tubing were used Iietnceti s tq i - rocks .I1 aiid and the t rap Id. It xv leaked in through the best of tithiiig apparatus. firiiily .-upported and thrii fusx l together i i i po- -ition. would iiot Iireak, .If a d A\- are large hollo~\--l)lowti <topcwk* with a (i-nim. liore. L is ail ortliiiary stopcock. These *t,ipc,lck* ~ l iou l t l lie carefully greased. so tliat 110 g r ~ a x i + left iii tlie bore, and then held iii place Tvitli claiiiI)s ( 1 ) to yeyei i t 1i)oseiiing aiid coiivqueiit leakage. Tlie overflow iaapillary tube f i n estalhli i i ig and tiiaiiitainiiig the ~avi i i i i i1 i i i B sliould lial-e a iuiifortii hore oi not iriore than 1 iiini. t o prevent l imkii ig of the mercury thread with cwiseqiiwt "Iyiiig don-11" of tlir gas iii the capillary during evncuatioii i i f tlie lia~otiieter. Tlie length of this capillary tulle slioiiltl l)e sucli that the difference hetweeii the wrfarc of the incr-

aii t l the t,ip of the buret i ? at leait 760 111111. Tl1t3 liorild be lielit a t the top of tlie Iiarornetcr as diortly r t.1 pre~ei i t the itiercury froin siphutiiiig hack. i- plaiined to use tlie Iiiiret a t pressures al)o\-e 1

atinoiphere. thc leiigtli of colritiiii B iiiust lie 1~roI)i)rtiiiiiatcIy greater.

111 Figure 3 is slion-n a more recent desigii, c~pecially hi- teiicletl fur uses where it is necebsary to measure the gas nt low pre.ssiires or \\-here it is desiralile to lie ahle to measurc the vapor pressure in tlic adjoining tem. Here the tiaroriict- ric columri is a straight tube parallel to the gas Iiuret arid i >

April 15, 1930 I-YDCSTRIAL d T D EAYGI:ISEERISG C'HEMISTRY 183

supported at, the bottom of the case in the same fashion as the buret. With this design i t is possible to measure very sinall gas volumes much more accurately by operating a t Ion- pressures. It, is the design of most universal appli- cation, and is inuch easier to make than the original. It requires a wide scale and even more careful leveling. If one is limited to a narrow scale, the original design is required.

Buret Case

Figure 2 s h o w in detail the buret case. The sides are made of i , ' g - in~h (2.2-em.) pine and the front and back each of four pieces of glass. The 150-cm. scale in the more ac- rurate types was engraved on whit,e celluloid fastened to a

*-inch (1.6.cm.) thick wooden strip, screwed to the nietal Iiraces. For less accurate work selected vooden 2-meter sticks iiiounted on wooden strips have been found satisfac- tory. i n the small types of liaro-buret it has been found cwivenient to support the mercury reservoir in a sliding l)racket, 0, mounted on the slide, S, fastened to the case. When the buret is used as part of a large set-up, it is inore convenient t o support the mercury reserv-oir on a ring clamp 011 a vertical steel rod fastened to the whole apparatus. The upper barometric column, B . in the type of buret shown i n Figures 1 and 2 is supported on the bracket, R (Figure 2), fastened hy hash plates to the scale.

Assembling

i n iiiaking the haro-buret the coluniii B, the capillary, and the side well D are fused together in a straight line and then bent, thus avoiding joints in tlie capillary in which gas might "lie down," The lower part of the barometer leading

s then fused on and the whole set in position in the case. Stopcock -11 is fused on to the gas buret and the buret is carefully cleaned, dried. and calibrated with distilled mercury (.$), The buret i? then placed in the case and supported by the slot in the base. Both the barometric column and the buret are then wired permanently in place. Stopcocks JI and A\7 are then fused on to the trap. L. rvliicli has been previously blown in the blast lamp. Calibrated thermometers are suspended in the case a l o n g d e the buret. The slots in the base and the side of the case are stopped with cotton to prevent air currents. A piece of plate glass covers tlie top of tlie case. The rubber tuliinp to the reser- 1-oir is wired in place. i t is also advisable to wire the rulilier tubing near the t rap permanently to the buret case, so that tlie t rap may not lie inadvert,ently broken. T o prei-ent smutting of the mercury by dust it is m l l to +topper the reservoir R with a liulb tube filled with glass ivool or cot,toii.

Operation

. ,

The stopcocks are greased and clamped and the whole liaro-buret is thoroughly dried by applying suction to the nioutli of the reservoir R and thus drawing air, dried by passage over potassium hydroxide and phosphorus pentoside 01' barium oxide (a), in through st,opcocks C, F , and L for a week. The buret should then be carefully leveled. Be- fore filling with mercury the reserwir R is lowered below the level of A\7 and the mercury slowly poured in; the entrapped air is removed by inanipulating the rubber tubing. Stop- cock L is clamped in a closed position and stopcocks J1 and S are opened. The buret, is evacuated through C and F , the mercury reservoir being kept a t a level sufficiently below S so tha t the mercury does not rise into S. \Then evacua- tion is practically complete, stopcock F is closed and clamped and reservoir R is sloivly raised, allowing t,he mercury t o rise in both K and B. The reservoir is raised further un t i l the mercury overflows down the capillary and forms a pool about' 1 em. deep in D; the reservoir is then quickly lowered

and the mercury column breaks. thus leaving a fair vaciiuiii in column B. The reservoir should then be lowered well below the base of the buret, so that the mercury in the baro- metric column is down to stopcock thus permitting gases adsorbed on the walls to evolve. After a few minutes tlie reservoir R is again raised and the gases are driven out as liefore. Great care should be taken to decrease the rate a t which the mercury rises as it approaches the top of tlie barometer, or the mercury will strike t,he constriction with huch force as to demolish it. A tiny bubble of air, on being forced d o w i the capillary against, atinospl-ieric pressure, teiids to .'lie down" in i t? v-liereas it is expauded so inuch if D is evacuated that it has t,o carry along with the mercury into D. This evacuating proce..; slioultl be repeated sewral times after allon-ing the buret to staiitl with the mercury level a t for several hours to remove atl>orlhed gases coin- pletely.

2 T d

Figure 1-Baro-Buret Figure 2-Buret Case

Each clay lieforc using the Iiuret it i; alsu atlvi5able to t w t tlie vacuum in B by driving the mercury over into D. If too Inucli mercury collects in D, it can hc forced back into the buret by admitting dry air through C, -ivhercupon tlre inercury xi11 be forced back into B until tlie difference in lerel in D and the top of B is equal to the atiriospheric pres- ?:lire. If a t any time it becomes tleiirable to renioye the mercury from the buret, air under slight pressure through C will force the mercury completely from D into B. This process should always be used since, if air is allowed to enter through S and thus rise in the barometer ieoluinii, i t will form a mercury hammer, which, lacking ail air cushion above i t , will strike the top of B so hard as to break it.

To use tlie baro-buret the gas t,o be measured is intro- duced through one of the capillary tubes of stopcock F by lowering R slowly, having stopcock -11 open. If desired, stopcock S may be closed during this operation, t'hus avoiding

184 dSd LYTICA L EDI T I O S Vol. 2 , s o . 2

moving the mercury in the barometric column. If i t is de- sired to flush out the buret with the gm, i t may be forced out again by raising reservoir R. Care must be taken, however, t o raise R very slowly as the mercury approaches stopcock F to avoid having the impact of the mercury break the stopcock. When a suitable sample of the gas has been introduced into the buret, F is closed and iY opened slowly. When the mercury levels in B and K have come to equilib- rium, the volume of the gas is read on the buret. The pressure on this gas is equal to the difference in height of the mercury columns in B and K as read on the scale directly behind them. Should i t be desirable to measure the ga. a t a particular pressure, R may be raised or lowered until the difference in height of the mercury in B and K equals the desired pressure, whereupon the volunie of gas may be read on the buret.

Measuring Smal l K--

Figure 3-New Design of Baro-Buret

Volumes

If the volume of the gas being measurcd is small a t 760 mm. prcs- wre , the gas may be more accuratdy meas- ured by expanding it to a l a r g e r volume (by lowering R ) and thus

Y I

measuring it a t a lower p r e s s u r e . f o r t h e most accurate results t h e distance between t h e m e r c u r y le i -e l s s h o u l d b e twice the h e i g h t of t h e g a s column in the buret. I n the measurement of e a s i 1 y c o n d e n s a b 1 e gases which tend to de- viate seriously from the ideal gas laws and suffer considerable adsorption o n t h e w a l l s of t h e buret, i t is advanta- geous to make themeas- urements a t lo^ pres- sure. By such tactics "vapors" may be meas- u r e d w i t h o u t intro- d u c i n g t o o great a n error.

To Remove a Gas f r o m t h e Baro-Buret

To remove a gas completely from a buret-as, for example, before introducing another gas-close A', open F , and raise R slo~vly until the mercury reaches F. Close this stopcock and lower R until the mercury in K is below the previous volume mark. This procedure will free gases that hare "lain down" between the buret wall and the mercury when the latter w s raised in the first operation. If R is raised slowly now, the gases will collect above the mercury in K as a small bubble, which can be easily forced through stop- cock F. This procedure is particularly advisable when measuring high-boiling-point gases and gases which are highly adsorbed b y glass.

Corrections

The pressure rending for accurate work should be corrected for the difference in gravity constant at the laboratory where

the readings are being made and a t sea level. I n this labora- tory the correct pressure reading (8) may be obtained by multiplying the observed pressure by 1.000384. n'eglect of this correction introduces an error of -0.04 per cent, Since the temperature of the mercury in the baro-buret is greater than 0" C., the true pressure a t 0" C. is less than the observed pressure. The corrected pressure may therefore be obtained by multiplying the observed pressure by a fac- tor wliich is the ratio of the density of the mercury a t the teniperature of the buret case to tha t a t 0" C. ( n ) .

For extremely accurate measurements the temperature correction for the scale should be known or determined, or else a scale engraved on glass should be used. The ideal scale n-ould be one engraved on glass silvered on the back. This mirror n-ould greatly reduce the error due to parallax.

I n calculating 1-0 it is Ire11 to include a correction for deviation from the gas laws, especially in the case of such an easily condensable gas as sulfur dioxide.

Errors and Limitat ions of Accuracy

It has bceii found in this lahoratory tha t the volume of a 100-cc. gas buret graduated to 0.2 cc. can be easily read to an accuracy of 0.05 cc., and by using a mirror or a mirror scale behind the buret to lessen the error due to parallax, the buret, n-ith care, may be read to 0.02 cc.-that i?, n-itli an accuracy of 1 part in 5000. I3y using a K h i t e bulbetl buret (12) doubtless this accuracy can be greatly increased. The pressure can easily be read to 0.2 m m . , thus gi\-ing an accuracy of approximately 1 part in 4000 when reading 1 atmosphere. According to the International Critical Tables (10) on the basis of six thousand observations, one ought, to be able to read a linear distance to 0.03 mm. This nould represent an accuracy in reading a pressure of 1 atmosphere of 1 part in 15,000. K i t h a cathetometer the pressure might be read to 1 part in 26,000, which would be particu- larly applicable in the ineasureiiient of vapor pressures, though it is doubtful if the temperature could be so controlled as to make such accuracy significant. l y e find no difficultj- in maintaining the temperature in t'he buret case within 0.1" C., tha t is, an accuracy of 1 part in 3000. However, i t is probable tha t some of these errors are positive and some negat'ive for any given experiment, so t h a t they may be considered to be to a certain estent self-compensating.

M a x i m u m Possible Error unde r Most Favorable Conditions for M i n i m u m Error

John A. Maurer, of this laboratory, has calculated as follows the maximum error possible under the most favorable conditions for minimum error in a single reading:

Perhaps the most important point which we encounter in attempting a comparison between the accuracy of measure- ments with the baro-buret and that of measurements with the ordinary gas buret is that the principle upon which the baro- buret is constructed makes i t necessary for the user to choose a particular one of an unlimited number of pressure-volume combinations a t which he might make his readings on a given sample of gas. It is clear that of all the choices possible there will be some one which makes the final error of the measurement a minimum. The present purpose is to discuss this question in connection with an attempt to find a definite expression for the accuracy.

It is easy to show that whenever we have three quantities, A , B , and C, connected by a relation of the form

and we wish to determine A by measuring B and C, we obtain the maximum precision consistent with our experimental methods if we can vary the ratio of B to C so as to make the experimental error in measuring B the same fraction of B as that in measur- ing C is of C.

For, if we represent the error, or perhaps it is better to say the

A = kBC (1)

April 15. 1930 ISDl'dTRI.lL A4AI-D ESGIAVEERISG CHE.IfI,STRY 185

uncertainty, in the different quantities by E,, Eb, and Ec, we have, remembering that Ea and E , are constants but E, is not,

aiid

The per cent uncertainty in A is

-4 + E, = k ( B 4- Eb) (c + E,)

E , = k (BE , + CEb + &E,)

( 2 )

(3)

100 E a - = 100 (: -2 + - + E;:) A

The last term on the right-hand side of (4) is negligibly small, so that we may say that in general the per cent uncertainty in A is equal to the sum of the per cent uncertainties in B and C.

To find the condition for making E, a minimum, we write (3) in the form:

and differentiate with respect to B, and then equate the right- hand side to zero. This gives

Writing A = kBC, we obtain

which is the result stated in the first paragraph.

the relation Applied to the case of the gas buret, where we make use of

1 VO = - Pi' PO

Equation 8 means that we should make our measurements under a pressure such that

EP - E , - _ - P V

With the ordinary gas buret it is difficult to do this without complicating our procedure in such a way as to introduce greater experimental errors, and measurements are usually made a t atmospheric pressure. We can easily measure a pressure in the neighborhood of 760 mm. with an accuracy greater than 0.1 per cent, but we must have very highly refined apparatus indeed if we are to measure the volume to within 1 per cent. Thus the accuracy of the pressure reading is of little value because of the large uncer- tainty in the volume reading.

n'ith the baro-buret, however, we can take our readings a t any desired pressure, so that it is a simple matter to fulfil the condition for maximum accuracy in the final result.

Just what the best pressure-volume combination will be for any given baro-buret depends upon how i t is set up, calibrated, and used. As an example, let us consider the conditions which apply to those in use a t the Morley Laboratory.

These baro-burets are made with the barometer tube the same size as the buret tube. The manner of reading the mercury level is the same for both tubes. Thus there is no need to cor- rect for capillary depression, and the uncertainty of the read- ing may be assumed to be the same in either tube. The cali- bration of the instruments is done with the aid of a cathetometer, but the readings are taken by eye and mirror scale. Thus the errors of calibration are negligible in comparison with those of regular use.

Suppose the uncertainty in reading the mercury level is i z and the area of cross section of the buret tube, A . If LI is the length of the tube occupied by the gas, V = AL1, E , = Ah, and E,/V = h/L1. The relative uncertainty of E p / P in the pressure reading is 2h/L2, where LZ is the length of the mercury column balanced by the pressure of the gas. The 2h appears because two readings are involved in determining the pressure, and i t is easily possible for the errors to be made so that they add. Then the condition E r / V = E J P reduces to h/L1 = 2hjL2, or LZ = 2L1; that is, we must adjust the leveling bulb so that the top of the mercury column in the barometer tube stands just as far above the upper end of the buret tube as the top of the column in the buret tube is below it. When this is done we have, from (4) and (8), that the per cent uncertainty in our determination of VO is 100 2h/L1.

It is not hard to put this in a form that can readily be applied to practical cases.

Suppose we have only 1 cc. of gas.

V 2 v L1 = -. P = L? = 2L1 = - A A

Substituting this value for P in the relation V = PUV"/P , we obtain

200 z/a JX h Per cent uncertainty in Vo = d P X

Since A = ' /a i~ D2, where D is the diameter of the buret tube, this may also be written

(101 100 4 G D i z Per cent uncertainty in Vu =

dm Thus the per cent uncertainty of a measurement varies directly as the diameter of the buret tube and inversely as the squire root of the quantity of gas being measured.

To show how this works out in practice, suppose VO = 60 cc. and that h, the uncertainty in reading the mercury level, is 0.02 cm. The area of cross section of the buret tube is not far from 2 sq. cm. This gives, by (Y),

Per cent uncertainty in VL = 200 4 4 2 (0.02) or 0.13 per cent, 4ETz

But if we are dealing with a small quantity of gas, say 1 cc. under standard pressure, the per cent uncertainty becomes

The uncertainty is still less than 1 per cent, whereas with the ordinary gas buret, assuming the same method of reading the mercury levels, the uncertainty in the volume reading alone is 4 per cent.

The above calculation has been carried out 011 the assumption that we wish to reduce to a minimum the uncertainty in a single measurement on a sample of gas. In carrying out a long investigation in which results are to be averaged, it is proba- bly desirable to adopt a slightly different procedure. If, as seems reasonable to the writer, the worker is as likely to read the mercury column too high as too low, the probability is 1 to 2 that the two errors involved in the pressure reading will cancel instead of add. Therefore, on the average the error of the pressure reading is not of the order of 2h, but of h. On this basis we should adjust the leveling bulb so as to make L1 = L?.

The temperature correct'ioii has not been taken into ac- count in the above discussion, because as far as it is concerned there is no difference b e t m e n the baro-buret and the ordi- nary gas buret.

Experience has shown that it, is not difficult to obtain a series of readings u-hich are consistent with each other to a much higher degree of accuracy. Nevertheless it is worth n-liile t o know how large the errors may become under the conditions of ordinary use.

Applications

~IEASUREMENT OF EXTERNAL \'oLums-The deterinina- tion of the volume of connecting tubing, or of an apparatus itself connected to the buret, is ordinarily a difficult matter, but is very easily accomplished by means of the baro-buret. To accomplish this, the buret K and the connecting tubing, whose volume is to be measured, are thoroughly evacuated and then filled with a dry, permanent gas, such that the volume Vi in the buret K shall be about 50 cc. at a pressure, Pi, of about 760 mm. Both pressure and volume are ac- curately observed with the stopcock F opened to the tubing or apparatus whose volume is to be measured. With stop- cock F open, reservoir R is lowered so tha t the new volume, LTZ, is approximately the full capacity of the buret, and the new pressure, Pz, and the volume, are accurately measured. Then i t is easily seen tha t Pi ( Vi + C) = P,( VZ + C), where

C' equals the constant volume to lie tleterniined. t h i.?

Solving

Pgv? - PITA c = P , - PJ

Obviously, the accuracy of such a measureiiient is iiiver>e!y proportional t,o the \-oluiiie to be measured, and of co1ir.p it is assumed that the buret K has been accurately calibrated.

I L L U ~ T R A T I O ~ OF DEYIATIOSS FROM G4s Laws-The baro- buret can readily be made the basis of an excellent experi- ment to demonstrate with such gases as carbon dioxide, sulfur dioxide, etc., the deviation froin the gas laws. Of course, the deviation with the so-called permanent gases is too small to be readily measured.

DETERMIKATIOS OF VAPOR PRESSLRE-TO determine the vapor pressure of a solid or liquid, the substance is placed in a bulb sealed to one of the capillaries connected to F using a baro-buret of the design shown in Figure 3. The buret is then used as the bulb of a Toepler pump, gas being pumped from the bulb into the buret, and by rotating the stopcock F 180 degrees and raising the buret the gas and vapor are driven out. Five or six punipiiigs are generally sufficient to give a constant pressure. The vapor tension is then equal to the difference in the levels of the mercury in B and K .

The last application illustrates how the buret may be used as a Toepler pump to pump out a small space. This

idea has been applied in a number of ways n-hich will be dir- cussed in separate papers: notably to a new method for gas

to the accurate analysis of gases with new apparatus for the determination of

adsorption 11y the static method: to an apparatus for the study of gas-solid equilibria in which pressure, volume, and con- centration are measured; to the rapid determination of the density of gases; to the measurement of gases evolved from reactions a t high temperatures; to the determination of the solubility of gases in liquids; as a laboratory dernoiistra- tioii of Ihy le ' s l a y to a inethod of obtaining accurate gas mixtures for the study of the critical phenomena of gas inixtnres: to the measurement of gases a t higher pressure>, etc.

Li terature Cited 1) Baume and Perrot, J . chim $/?ye. , 11, .57 (19133. ) Bone, Pvor Chem. S O L , 14, 154 (1898). ) Bone and Ivheeler, .I. .Tor. Cheni. I n d . , 27, 10 (19G8i. \ Booth and Jones, IND. ESG. CI%E>r., 19, 104 113371.

( 5 ) Booth and McIn ty re , I b i d . , Anal Ed.. 2, 12 (1930). (6) Frankland and Ivard, J . Chem. Sot. , 6, 197 (1854). (7) Germann, J . . l m Chem. SO<., 36, 24.56 (1914) . is) Germann and Booth. J . f h y s . Cketn , 21, 87 ( 1 9 l i i . (9) International Critical Tables, Vol. I , p 68.

(101 I b i d . . p. 94. (11) White, J . . lm. Chem. SOC. , 22, 313 t , l ' J O O ) . 112: White, "Gas and F u e l Anal.

*

Corrections for Standard Solutions of Inconvenient Strengths'

Selma Gott l ieb

DIVISIOX O F S A S I T A T I O Y . KASS.\S ST.\TE B o A n D Of FIEALTH. A S D t .SI \ .ERSITY OF KANSAS, LAU'RESCE. KASS

S ?IlAKISC; a large number of volumetric aiialy<es using the same standard solut'ion, it is of course very con- \-enient to adjust the solution to such a strength tha t the

calculat,ion of results is simplified as much as poesihle. Hex- ever, it' seems scarcely worth while to make careful atljust- nients of those solutions which change strength rapidly. when t'he process will h a r e to be repeated in a short tinie. The following suggestion is therefore offered to simplify the correction of buret readings for such wlutions to t1io.e corresponding to the strength desired.

This niethod was originally applied to a sodiuin thiosulfate solut,ion used in the dissolved-oxygen determinations rp- quired in biocheniical oxygen tlernaiid tests on sewage, antl intended to be 0.025 norinal. When a solution of this exact strength is used. the number of cubic ceiitiiiietrrs of it re- quired in titrating a 200-cc. portion of the treated liquid is directly equal to the parts per niillion of di.ssolvet1 oxygen present. Because of dehydration of the sodium tliioiulfatc crystals used, the solution as made in one case was 0.02531 normal. or 1.0124 tinies the intended strength. ant1 because of the instability of sodiuiii thiosulfate solutions it wa.; thought desirable to work out a simple niethod of applying the necessary correction, rather than to adjust it to the desired tit'er.

If r is the ratio of the strength of the solution used to that of the solution desired, R: tlie buret reading, and c the cor- rection needed to bring the buret, reading to tha t correspond- ing to the strength desired, the following relation will he obvious:

1 Received January 16, 1930.

Y S = s * c * r

and .T = - r - 1

The sign of c will lie positive when r i y greater tliaii OIIP xii(l

negative when T is less than one. By substituting into the equation successive values of r

and the value of T as obtained froin the Ptantlartlizatioii ( ~ i the mlution in question, the corresponding values of .2: can be calculated. The value of ,2: obtained when c is 0.005 rppre3ents tlie l o w s t buret reading to which it i< necehhary to add 0.01 cc. as a correction. The nest calculated \-aluc~ of .E, n-hen c is 0.0149, mark; the end of the range for wliicli a correction of 0.01 cc. is sufficient. Similarly, when r i i 0.0249. .c represent.; the end of the range to which a corrcction of 0.02 cc. is applicable, etc.

The corrected volume can then be readily found froiii thc table prepared for the solution used, more rapidly than with a slide rule, antl inore accurately.

R.ISGE OF CORRECTIOS Connscrrux c ) L-alues of u .Idd

0 40 - 1 . 2 0 1 21 - 2 00 2 01 - 2 81

6 85 - 7 65 7 66 - 8 46 8 47 - 9 27

0 01 0 02 0 03

0 09 0 10 0 11

hlthough the application ~f this equation is lirnited. i t is a inarked time saver in the cases in which it can be used. I t is useful, for instance, when Kjeldahl determinations are made with acid and alkali solutions that are not exactly equiva- lent, and in many other routine volumetric det,errninations.